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Is the following number rational or irrational? (0.3)/(0.9) Choose 1 answer: (A) Rational (B) Irrational

Is the following number rational or irrational?\newline0.30.9\frac{0.3}{0.9}\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational

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Full solution

Q. Is the following number rational or irrational?\newline0.30.9\frac{0.3}{0.9}\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational
  1. Evaluate the fraction: Evaluate (0.3)/(0.9)(0.3)/(0.9).\newline(0.3)/(0.9)=0.3÷0.9(0.3)/(0.9) = 0.3 \div 0.9\newlineTo simplify the fraction, we can multiply both the numerator and the denominator by 1010 to get rid of the decimal points.\newline(0.3×10)/(0.9×10)=3/9(0.3 \times 10) / (0.9 \times 10) = 3/9
  2. Simplify the fraction: Simplify the fraction 39\frac{3}{9}. \newline39\frac{3}{9} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 33. \newline(33)/(93)=13(\frac{3}{3}) / (\frac{9}{3}) = \frac{1}{3}
  3. Identify the type of number: Identify whether 13\frac{1}{3} is a rational or irrational number.\newline13\frac{1}{3} is a fraction where both the numerator and the denominator are integers, and the denominator is not zero. Therefore, 13\frac{1}{3} is a rational number.

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